/* @(#)k_cos.c 1.3 95/01/18 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

/*
 * __kernel_cos( x,  y )
 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
 * Input x is assumed to be bounded by ~pi/4 in magnitude.
 * Input y is the tail of x. 
 *
 * Algorithm
 *	1. Since cos(-x) = cos(x), we need only to consider positive x.
 *	2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
 *	3. cos(x) is approximated by a polynomial of degree 14 on
 *	   [0,pi/4]
 *		  	                 4            14
 *	   	cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
 *	   where the remez error is
 *	
 * 	|              2     4     6     8     10    12     14 |     -58
 * 	|cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
 * 	|    					               | 
 * 
 * 	               4     6     8     10    12     14 
 *	4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
 *	       cos(x) = 1 - x*x/2 + r
 *	   since cos(x+y) ~ cos(x) - sin(x)*y 
 *			  ~ cos(x) - x*y,
 *	   a correction term is necessary in cos(x) and hence
 *		cos(x+y) = 1 - (x*x/2 - (r - x*y))
 *	   For better accuracy when x > 0.3, let qx = |x|/4 with
 *	   the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
 *	   Then
 *		cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
 *	   Note that 1-qx and (x*x/2-qx) is EXACT here, and the
 *	   magnitude of the latter is at least a quarter of x*x/2,
 *	   thus, reducing the rounding error in the subtraction.
 */

package kotlin.math.fdlibm


private const val one = 1.00000000000000000000e+00 /* 0x3FF00000, 0x00000000 */
private const val C1 = 4.16666666666666019037e-02 /* 0x3FA55555, 0x5555554C */
private const val C2 = -1.38888888888741095749e-03 /* 0xBF56C16C, 0x16C15177 */
private const val C3 = 2.48015872894767294178e-05 /* 0x3EFA01A0, 0x19CB1590 */
private const val C4 = -2.75573143513906633035e-07 /* 0xBE927E4F, 0x809C52AD */
private const val C5 = 2.08757232129817482790e-09 /* 0x3E21EE9E, 0xBDB4B1C4 */
private const val C6 = -1.13596475577881948265e-11 /* 0xBDA8FAE9, 0xBE8838D4 */

internal fun __kernel_cos(x: Double, y: Double): Double {
    var a: Double
    var hz: Double
    var z: Double
    var r: Double
    var qx: Double = 0.0
    var ix: Int
    ix = __HI(x) and 0x7fffffff    /* ix = |x|'s high word*/
    if (ix < 0x3e400000) {            /* if x < 2**27 */
        if ((x.toInt()) == 0) return one        /* generate inexact */
    }
    z = x * x
    r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * C6)))))
    if (ix < 0x3FD33333)            /* if |x| < 0.3 */
        return one - (0.5 * z - (z * r - x * y))
    else {
        if (ix > 0x3fe90000) {        /* x > 0.78125 */
            qx = 0.28125
        } else {
            qx = doubleSetWord(d = qx, hi = ix - 0x00200000)    /* x/4 */
            qx = doubleSetWord(d = qx, lo = 0)
        }
        hz = 0.5 * z - qx
        a = one - qx
        return a - (hz - (z * r - x * y))
    }
}
